1. Field of the Invention
The present invention relates to an image processing apparatus, an image processing method and an information recording medium for processing an input image by Fourier transform.
2. Description of the Related Art
Conventionally, a method for image compression or the like has ordinarily been used in which an original image is divided into domains and a feature of each domain is extracted by discrete cosine transform of each domain. If an original image to be processed by such a method is input to a processing apparatus by an optical system, the optical system is moved so as to image divided domains of the image one after another.
The method of dividing an original image into domains and performing discrete cosine transform of each domain as described above achieves a high compression ratio but entails occurrence of considerable block-like noise at the time of inverse transform. Also, because of processing with respect to each domain, it is difficult to extract widely viewed features of an entire original image. Further, the conventional method of processing an image by moving an optical system and imaging divided domains of the image one after another is disadvantageous because a considerably long time is required for the troublesome image processing.
In view of the above-described circumstances, an object of the present invention is to provide an image processing apparatus capable of extracting widely viewed features of an entire image and speedily performing image processing, and a method and an information recording medium for such processing.
According to the present invention, the above-described object is accomplished by performing a process in which an entire original image is input at a time and transformed by Fourier transform; an amplitude distribution of a signal obtained by the Fourier transform is replaced with a predetermined function using the distance from a center of a frequency plane as a parameter; and an image corresponding to the original image is formed by inverse Fourier transform from a phase distribution of points obtained by the Fourier transform and from an amplitude distribution obtained by the above-mentioned replacement.
That is, to perform this process of the present invention, there is provided an information processing apparatus including an image input section for inputting an original image, a transform section for performing Fourier transform of the input image, an amplitude replacement section for replacing an amplitude distribution of a signal obtained by the transform section with a predetermined function approximated to the amplitude distribution and using the distance from a center of a frequency plane as a parameter, and an inverse transform section for forming an image corresponding to the original image by inverse Fourier transform from a phase distribution of points obtained by the transform section and from an amplitude distribution obtained by the replacement performed by the amplitude replacement section.
According to the present invention, there is also provided an image processing method including an image input step of inputting an original image, a transform step of performing Fourier transform of the input image, an amplitude replacement step of replacing an amplitude distribution of a signal obtained by the Fourier transform with a predetermined function approximated to the amplitude distribution and using the distance from a center of a frequency plane as a parameter, and an inverse transform step of forming an image corresponding to the original image by inverse Fourier transform from a phase distribution of points obtained by the Fourier transform and from an amplitude distribution obtained by the replacement in the amplitude replacement step.
According to the present invention, there is also provide an information recording medium having an image processing program stored therein, the image processing program being readable and executable by a computer which performs a process including an image input step of inputting an original image, a transform step of performing Fourier transform of the input image, an amplitude replacement step of replacing an amplitude distribution of a signal obtained by the Fourier transform with a predetermined function approximated to the amplitude distribution and using the distance from a center of a frequency plane as a parameter, and an inverse transform step of forming an image corresponding to the original image by inverse Fourier transform from a phase distribution of points obtained in the transform step and from an amplitude distribution obtained by the replacement in the amplitude replacement step.
According to the present invention, the above-mentioned predetermined function is, for example, a fractional function using the distance from the center of the frequency plane as a parameter. According to the present invention, the values of the real parts of points of the image formed by the inverse Fourier transform are changed so that the real part of each point is not smaller than 0. Further, a trial function:
f(k)=a/(kb+h)
is used as an optimal approximation to the second power of an amplitude distribution of each of the points on the Fourier complex plane.
According to the present invention, the above-described object is also accomplished by performing a process in which an original image is input and transformed by Fourier transform; a fractal dimension of an amplitude distribution with respect to the distance from the center of a Fourier complex plane of a signal obtained by the Fourier transform is calculated; an amplitude distribution of points on the Fourier replaced is replaced with a predetermined function using the fractal dimension; and an image corresponding to the original image is formed by inverse Fourier transform from a phase distribution of the points obtained by the Fourier transform and from an amplitude distribution obtained by the above-mentioned replacement.
According to the present invention, to perform this process, there is provided an image processing apparatus including an image input section for inputting an original image, a transform section for performing Fourier transform of the input image, a fractal dimension calculation section for calculating a fractal dimension of an amplitude distribution with respect to the distance from a center point of a Fourier complex plane obtained by the transform section, an amplitude replacement section for replacing an amplitude distribution of points on the Fourier complex plane obtained by the transform section with a predetermined function using the fractal dimension calculated by the fractal dimension calculation section, and an inverse transform section for forming an image by inverse Fourier transform from a phase distribution of the points on the Fourier complex plane obtained by the transform section and from an amplitude distribution obtained by the replacement performed by the amplitude replacement section.
According to the present invention, there is also provided an image processing method including an image input step of inputting an original image, a transform step of performing Fourier transform of the input image, a fractal dimension calculation step of calculating a fractal dimension of an amplitude distribution with respect to the distance from a center point of a Fourier complex plane obtained by the Fourier transform, an amplitude replacement step of replacing an amplitude distribution of points on the Fourier complex plane obtained by the Fourier transform with a predetermined function using the fractal dimension, and an inverse transform step of forming an image by inverse Fourier transform from a phase distribution of the points on the Fourier complex plane obtained by the Fourier transform and from an amplitude distribution obtained by the replacement in the amplitude replacement step.
According to the present invention, there is also provided an information recording medium having an image processing program stored therein, the image processing program being readable and executable by a computer which performs a process including an image input step of inputting an original image, a transform step of performing Fourier transform of the input image, a fractal dimension calculation step of calculating a fractal dimension of an amplitude distribution with respect to the distance from a center point of a Fourier complex plane obtained by the Fourier transform, a replacement step of replacing an amplitude distribution of points on the Fourier complex plane obtained by the Fourier transform with a predetermined function using the fractal dimension, and an inverse transform step of forming an image by inverse Fourier transform from a phase distribution of the points on the Fourier complex plane obtained by the Fourier transform and from an amplitude distribution obtained by the replacement in the amplitude replacement step.
According to the present invention, the amplitude distribution is replaced with, for example, a function shown as xcex1/fd where f is the spatial frequency of the input image corresponding to the distance from the center point of the Fourier complex plane, d is the fractal dimension, and xcex1 is a predetermined constant. According to the present invention, the values of the real parts of points of the image formed by the inverse Fourier transform are changed so that the minimum of the real parts of the points is not smaller than 0.
Further, according to the present invention, the above-described object is accomplished by performing a process in which an original image is input and transformed by Fourier transform; an amplitude distribution of points on a Fourier complex plane obtained by the Fourier transform is replaced with a predetermined function; equivalent smoothing transform of a phase distribution of the points on the Fourier complex plane obtained by the Fourier transform is performed in one of a direction along the abscissa and a direction along the coordinate; differences in the phase distribution processed by the equivalent smoothing transform are extracted along the direction of the smoothing transform; secondary differences in a phase distribution obtained by the first difference extraction are further extracted; an amplitude distribution obtained by the replacement with the predetermined function and the secondary differences in the phase distribution are combined with each other; the amplitude distribution is replaced with the result of the above-mentioned combining; and an image corresponding to the original image is formed by inverse Fourier transform from the phase distribution of the points on the Fourier complex plane obtained by the Fourier transform and from the amplitude distribution obtained by the above-mentioned combining.
To perform this process according to the present invention, there is provided an image processing apparatus including an image input section for inputting an original image, a transform section for performing Fourier transform of the input image, an amplitude replacement section for replacing an amplitude distribution of points on a Fourier complex plane obtained by the transform section with a predetermined function, a smoothing transform section for performing equivalent smoothing transform of a phase distribution of the points on the Fourier complex plane obtained by the transform section in one of a direction along the abscissa and a direction along the coordinate, a difference detection section for extracting differences in the phase distribution of the points on the Fourier complex plane processed by the equivalent smoothing transform performed by the smoothing transform section, the differences being extracted along the direction of the smoothing transform, a secondary difference detection section for further extracting differences in a phase distribution obtained by extracting differences by the difference detection section, a combining section for combining an amplitude distribution obtained by the replacement performed by the amplitude replacement section, and the secondary differences in the phase distribution detected by the secondary difference detection section, the combining means replacing the amplitude distribution with the result of the above-mentioned combining, and an inverse transform section for forming an image corresponding to the original image by inverse Fourier transform from the phase distribution of the points on the Fourier complex plane obtained by the transform section and from the amplitude distribution obtained by the combining performed by the combining means.
According to the present invention, there is also provided an image processing method including an image input step of inputting an original image, a transform step of performing Fourier transform of the input image, an amplitude replacement step of replacing an amplitude distribution of points on a Fourier complex plane obtained by the Fourier transform with a predetermined function, a smoothing transform step of performing equivalent smoothing transform of a phase distribution of the points on the Fourier complex plane obtained by the Fourier transform in one of a direction along the abscissa and a direction along the coordinate, a difference detection step of extracting differences in the phase distribution processed by the equivalent smoothing transform, the differences being extracted along the direction of the smoothing transform, a secondary difference detection step of further extracting differences in a phase distribution obtained by extracting differences in said difference detection step, a combining step of combining an amplitude distribution obtained by the replacement with the predetermined function, and the secondary differences in the phase distribution, and replacing the amplitude distribution with the result of the above-mentioned combining, and an inverse transform step of forming an image corresponding to the original image by inverse Fourier transform from the phase distribution of the points on the Fourier complex plane obtained by the Fourier transform and from the amplitude distribution obtained by the above-mentioned combining.
According to the present invention, there is also provided an information recording medium having an image processing program stored therein, the image processing program being readable and executable by a computer which performs a process including an image input step of inputting an entire original image at a time, a transform step of performing Fourier transform of the input image, an amplitude replacement step of replacing an amplitude distribution of points on a Fourier complex plane obtained by the Fourier transform with a predetermined function, a smoothing transform step of performing equivalent smoothing transform of a phase distribution of the points on the Fourier complex plane obtained by the Fourier transform in one of a direction along the abscissa and a direction along the coordinate, a difference detection step of extracting differences in the phase distribution processed by the equivalent smoothing transform, the differences being extracted along the direction of the smoothing transform, a secondary difference detection step of further extracting differences in a phase distribution obtained by extracting differences in the difference detection step, a combining step of combining an amplitude distribution obtained by the replacement with the predetermined function, and the secondary differences in the phase distribution, and replacing the amplitude distribution with the result of the combining, and an inverse transform step of forming an image corresponding to the original image by inverse Fourier transform from the phase distribution of the points on the Fourier complex plane obtained by the Fourier transform and from the amplitude distribution obtained by the combining.
According to the present invention, the above-mentioned predetermined function is, for example, a 1/f function using as a parameter a spatial frequency f of the input image corresponding to the distance from the point of the Fourier complex plane. The above described xe2x80x9cdifference(s)xe2x80x9d can be substituted by xe2x80x9cdifferential(s)xe2x80x9d. According to the present invention, in the smoothing transform, 2nxcfx80 (n: integer) is added to each of the points starting from a phase value on one of the coordinate and the abscissa of the Fourier complex plane such that the amount of change between the phase values of each pair of the points adjacent to each other in one of a direction along the coordinate and a direction along the abscissa is within the range of xc2x1xcfx80. Further, the Fourier transform and/or inverse Fourier transform are performed by using a fast Fourier transform algorithm.